Hohenheimer Agrarökonomische Arbeitsberichte
Quality Ambiguity and the Market
Mechanism for Credence Goods
Dietrich Benner
Arbeitsbericht Nr. 9
Institut für Agrarpolitik und Landwirtschaftliche Marktlehre (420)
Universität Hohenheim, 70593 Stuttgart
Veröffentlichung des Institutes für
Agrarpolitik und Landwirtschaftliche Marktlehre der Universität Hohenheim
ISSN 1615-0473
Herausgeber:
Institut für Agrarpolitik und Landwirtschaftliche Marktlehre
Universität Hohenheim (420)
70593 Stuttgart
Tel.: 0711/459-2599
Fax.: 0711/459-2601
e-mail: [email protected]
Gesamtherstellung:
Institut für Agrarpolitik und
Universität Hohenheim (420)
70593 Stuttgart
Landwirtschaftliche
Marktlehre
Quality Ambiguity and the Market Mechanism for Credence Goods
D. Benner*
Institut für Agrarpolitik und Landwirtschaftliche Marktlehre
Universität Hohenheim
August 2004
Dr. Dietrich Benner war wissenschaftlicher Mitarbeiter am Institut für Agrarpolitik und Landwirtschaftliche
Marktlehre der Universität Hohenheim
Quality Ambiguity and the Market
Mechanism for Credence Goods
Dietrich Benner
Abstract
With credence goods consumers cannot judge actual quality neither before purchase
(ex ante) nor after purchase (ex post). Trust has to replace own examination and
verication. Applying Choquet-Expected Utility theory, a general model of credence
goods is developed which takes the problem of trust explicitly in its view and generalizes the problem of quality uncertainty on the 'market for lemons' of Akerlof (1970)
to 'quality ambiguity' with credence goods. The model shows the market mechanism
only performing well in providing credence goods when consumers' trust in given
information is not too low. With trust too low, sellers of credence goods will be
driven out of the market by trust induced adverse selection. In market equilibrium
prices will always be lower compared to equillibrium prices for experience goods.
Journal of Economic Literature Classi cation Numbers: C72, D81, D82.
Key words:
credence goods, asymmetric information, quality ambiguity, quality
uncertainty, adverse selection, ambiguity, choquet expected utility
Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2
Adverse Selection with credence goods . . . . . . . . . . . . . . . .
7
2.1
The model . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.2
The equilibrium conditions . . . . . . . . . . . . . . . . . .
10
2.2.1
Pooling equilibrium . . . . . . . . . . . . . . . . .
11
2.2.2
Semi-pooling equilibrium . . . . . . . . . . . . . .
15
Discussion of the equilibrium conditions . . . . . . . . . . .
19
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2.3
3
Appendix
A
Adverse selection with experience goods . . . . . . . . . . . . . . .
29
A.1
Separating equilibrium . . . . . . . . . . . . . . . . . . . . .
31
A.2
Pooling equilibrium . . . . . . . . . . . . . . . . . . . . . .
32
A.3
Semi-Pooling equilibriums . . . . . . . . . . . . . . . . . . .
33
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
1 Introduction
Since Akerlof (1970) has given a theoretical understanding of adverse selection
the market mechanism under asymmetric information caused by quality uncertainty has constituted a main focus of research in economics of information
(for an comprehensive overview see textbooks on industrial organization e.g.
Tirole (1988), Carlton and Perlo
(1994), Shy (1995).) However, all models
introduced so far refer to markets for goods with a quality distribution assumed to be known or to be deducible from former experience, i.e. quality
itself must be veriable at least after purchase. In economics of information
goods satisfying this condition are classied either as search goods or as experience goods (Nelson (1970), Nelson (1974)). Beside many goods which fall
into this categories (e.g. canned food), there is a growing range of goods for
which quality is not known even after purchase, e.g. goods with quality specied in terms of the production process like the good's country-of-origin, the
welfare of producing animals, or the use of hormones in keeping animals. According to Darby and Karni (1973) a good for which actual quality cannot
be veried neither before purchase (ex ante) nor after purchase (ex post) is
called credence good (cf. table 1).
quality is veriable
ex ante
ex post
yes
yes
no
yes
no
no
type of good
search good
experience good
credence good
Table 1. Asymmetric Information and types of goods
2
This paper is about asymmetric information with credence goods. With credence goods a specic new aspect of asymmetric information arises which is
not yet captured by the models dealing with quality uncertainty. Since consumers cannot verify any given information on their own even after purchase
with credence goods it is trust in received information which has to replace
own examination and verication.
Whereas empirical studies have shown consumers' awareness of credence goods
(Lynch and Schuler (1991), Arnthorsson et al. (1991)), there is only a small
theoretical literature dealing with credence goods. The models presented so
far mainly di
er along two dimensions. Firstly, the models capture a good's
credence component in di
erent ways. On the one hand, the credence component is assumed to arise from so called expert services. With expert services an
expert both provides the service and determines the amount of treatment so
that the customer cannot verify the service provided at all (Darby and Karni
(1973), Pitchik and Schotter (1997), Taylor (1995), Wolinsky (1995), Emons
(1997), Emons (2001)). On the other hand, the credence component is assumed
to be caused by aspects of the production process, which cannot be observed
by consumers. (Schmutzler (1992), Feddersen and Gilligan (2001)). Secondly,
the models make di
erent assumptions on how information, which consumers
cannot determine on their own, is provided. Provision of information is either modeled by additional sources of information which replace consumers'
own evaluation (Schmutzler (1992), Feddersen and Gilligan (2001)) or by the
ability of consumers in getting the information indirectly (Wolinsky (1995),
Emons (1997), Emons (2001)). Beside all di
erences, in all frameworks existence of a market equilibria for which a transaction takes place is only made
possible by a portion of trust coming along either by the trustworthiness of
3
the seller himself or by a guarantee of a third party which can be trusted.
However, this aspect of trust is assumed only implicitly and cannot be made
explicit in the assumptions for any of these models. As a consequence, the
specic dimension of credence goods has not yet captured and the inuence
of trust in market performance cannot be analyzed directly.
type of good
decision situation
search good
;!
experience good ;!
credence good ;!
certainty
risk
uncertainty
Table 2. Typ of good and decision situation
To overcome the lack of the models developed so far this paper presents a
model which considers the specic decision theoretic conditions given with credence goods.1 The three types of goods di
er in the way beliefs about a good's
actual quality are deduced (Steenkamp (1990)). With search goods quality can
be deduced by pure inspection before consumption with certainty leading to
decisions under certainty. For experience goods quality can be veried at least
after consumption. Thus, beliefs are given by a probability distribution over
quality and are known ex ante or can at least be deduced from own experience after consumption. Decisions concerning experience goods therefore correspond to decisions under risk. Quality of credence goods is not known even
after consumption. There is no basis for beliefs represented by probabilities
(Caswell and Mojduszka (1996, p. 1250)) and decisions with credence goods
therefore are based on uncertainty.
Considering the given characterization (cf. table 2) the formal analysis of
credence goods amounts to the question how to formalize decisions under un4
certainty arising from credence goods within decision theory. The leading theory to model decisions under uncertainty is subjective expected utility theory
(SEU) as rstly developed by Savage (1954). Within SEU subjective probabilities can always be deduced from revealed decisions (Savage (1972, p. 51)) and
include all aspects of uncertainty, i.e. both the impreciseness and the uncertainty of decision makers' knowledge about the uncertainty of the event itself
(Savage (1972, p. 3)). Taking subjective probabilities generally as a basis for
formalization of decision situations, there is no sense in distinguishing risk
from uncertainty or experience goods from credence goods, respectively, since,
in this case, probabilities are never unknown to the decision maker (Camerer
and Weber (1992, p. 326)).
However, uncertainty given with credence goods is just characterized by the
lack of any information about a good's quality and beliefs or probabilities,
respectively. Thus, for a adequate representation of credence goods within decesion theory a equal-treating of uncertainty and risk according to SEU is not
appropriate. The distinction between risk and uncertainty, i.e. between known
and unknown probabilities, has already been stressed before axiomatization
of SEU (Knight (1921)), but has been widely discussed in decision theory
only since the direct attack on the axioms of SEU by the Ellsberg-Paradoxa
(Ellsberg (1961)). Together with subsequent experimental studies (for a broad
overview cf. Camerer and Weber (1992), Payne et al. (1992), Camerer (1995)),
the Ellsberg-Paradoxa show that SEU is not sucient to represent decision
situations for which clear cut information is missing. It is just the lack of precise information relevant to a decision which contradicts the representation
of decision makers' beliefs by probabilities both in the Ellsberg-paradoxa and
with credence goods. In the given context, decision situations are uncertain for
5
which no probabilities can be deduced because of a lack of information. This
are just the situations for which Knight (1921) uses the term uncertainty and
Ellsberg (1961) introduced the term ambiguity. It is then just the distinction
between risk and ambiguity which captures the essential aspect of the difference between experience goods as decisions under risk and credence goods
as decisions under ambiguity. As a consequence, we suggest to use the term
quality ambiguity when considering credence goods. Then, refering to situations with experience goods, it would be more precisely to speak of quality
risk instead of quality uncertainty.
Di
erent approaches to cope with ambiguity in formal models have been
given (Camerer and Weber (1992)). Our paper presents a model of quality uncertainty with credence goods which utilizes Choquet Expected Utility theory (Gilboa (1987), Schmeidler (1989)) and its application to game
theory (Dow and Werlang (1994), Eichberger and Kelsey (1994), Eichberger
and Kelsey (1999)). The model extents the lemons' market of Akerlof (1970)
by referring to decisions concerning credence goods as decisions under ambiguity. Consumers' beliefs over sellers' behavior are represented by nonadditive probabilities (capacities), and market behavior is modeled as a noncooperative signalling game under ambiguity with equilibria given by the concept of Dempster-Shafer equilibrium (DSE) under uncertainty (Eichberger and
Kelsey (1999), Ryan (2002)).
6
As a main result, the crucial role of trust in given information becomes obvious.
For credence goods the lack of trust is an additional new source for market
failure with trust too low, sellers of credence goods will be driven out of the
market by trust induced adverse selection even when this quality itself would
be accepted if it could be judged after purchase, i.e. for experience goods.
Even if a market for credence goods exists equilibrium prices always will be
lower for credence goods than for experience goods.
The remainder of the paper is organized as follows. In section 2 our model of a
market for credence goods is presented. Market behavior is modeled as a noncooperative signalling game under ambiguity for which the aspect of trust
is captured by representing consumers' beliefs over quality by non-additive
probabilities (capacities). Section 3 summarizes the conclusions of the model.
2 Adverse Selection with credence goods
2.1 The model
Consider a market for a credence good for which quality is the only characteristic relevant for a buying decision. The transaction process between sellers
and consumers is modeled as a signalling game between a sender (seller) and
a receiver (consumer). Three di
erent exogenous given qualities are o
ered on
the market: A good can be of low (L), medium (M) or high (H) quality. Since
only the seller knows the actual quality before a purchase there is asymmetric information with regard to quality. The only information available for the
consumer is the distribution of quality which is given by the exogenous probabilities (H ) = q , (M ) = q , and (L) = q with P 2f
H
M
L
7
t
L M H
g
(t) = 1.
Throughout the section it is assumed that the good is a credence good, i.e.
the consumer holds beliefs over the good's quality which are ambiguous.
The seller and the consumer di
er from each other by their valuation of di
erent qualities. With parameters a and a (a a 2 IR) the consumer values
the quality t 2 fL M H g at a t and the seller at a t. It is assumed that the
S
C
S
C
C
S
consumer does not value a specic quality level higher than the seller values
the next higher quality level, i.e. CS < and CS < . Additionally, the consumer values a given quality always higher than the seller, i.e. a < a . Thus,
a purchase would be desirable if the consumer was knowing true quality.
a
M
a
H
a
L
a
M
S
C
The di
erent qualities are represented by seller types, i.e. the set of seller types
is given by T1 = fL M H g. Each seller type can o
er the good and ask for a
price p 2 IR+ or can withdraw from the market (n ), i.e. the seller's strategy
set S1 is given by S1 = IR+ fn g. The consumer observes the prices and can
reject or accept the o
er, i.e. his strategy set S2 is given by S2 = fyes nog.
p
p
If the consumer rejects an o
ered price p he yields zero utility and the seller
yields a utility of a t (t 2 T1). Given a quality t, accepting an o
er the
consumer yields an utility of a t ; p and the seller receives the price p. By
withdrawing from the market at a quality t, the consumer always gets zero
S
C
utility and the seller yields a utility of a t.
S
The consumer's beliefs about the behavior of the seller and the quality of
the o
ered credence good, i.e. the seller's type, are represented by a capacity
1 : S1 T1 ;! 0 1] (Eichberger and Kelsey (1999)). Since only the consumer
has got incomplete information the seller's beliefs about the behavior of the
consumer are represented by additive probabilities, i.e. 2 (yes) 2 f0 1g and
2 (no) 2 f0 1g with 2 (yes) + 2(no) = 1.
8
Within our model there are two reasons for representing the beliefs by a simple capacity (Eichberger and Kelsey (1994)), i.e. a capacity whose value for
an event is given by the product of an additive probability for this event and
a weighting parameter . On the one hand, by representing trust in given
information by a parameter it is possible to analyze the impact of trust in
the behavior of the players directly. On the other hand, analyzing the resulting game is more manageable and the results can be compared with results
given by models for experience goods straight forwardly: In equilibrium the
probabilities of the game in additive probabilities can be used in the denition of simple capacities (Eichberger and Kelsey (1996)), i.e. the additive
probabilities of the capacities are given by the corresponding game under risk
for experience goods (cf. appendix A). By utilizing simple capacities credence
goods and experience goods di
er in the weighting parameter as a measure
of trust in the given probabilities. With credence goods lies in the half-open
interval 0 1), and the situation with experience goods is given by = 1.
With an additive probability distribution : S1 T1 ;! 0 1] and a parameter
2 0 1] the consumer's beliefs 1 are given
8
>>
>> (A) A S1 T1
>>
<
1 (A) = >
if
>>
>>
>: 1
A = S1 T1
(1)
Additionally, it is assumed that (f(s1 t) : s1 2 S1 g) = q (t 2 T1 ), i.e. the
marginal distribution of is equal to the distribution over types. Since the
probabilities are given by the corresponding game with additive probabilit
9
ties in equilibrium they are determined by the additive distributional strategies
played in equilibrium. As a measure of trust in the probabilities , the parameter also represents trust in the given information about the distribution of
types, i.e. the quality distribution.
2.2 The equilibrium conditions
Equilibrium strategies can be distinguished according to the seller's types
playing same prices (pooling or semi-pooling equilibrium) or playing di
erent
prices (separating equilibrium). However, separating equilibriums can be disregarded: If the seller plays a di
erent price p^ for every type t^ 2 fL M H g
the updated beliefs are given by
t
8>
>>
q
t = t^
>> 1 ; (1 ; q )
><
1
(tjp^) = >
if
>
>>
>>
0
otherwise
:
t
t
t
(2)
For > 0 the consumer can distinguish the seller types and would accept a
high price. Thus, there is an incentive for the low and medium seller type to
play a high price as well. Analysis therefore will be restricted to pooling and
semi-pooling price o
ers of the seller.
So far, the buying decision of the consumer depends on the beliefs for receiving
a certain quality after observing a price o
er. If he rejects an o
ered price p
he receives zero utility. Thus, he rejects if this price o
er is greater than the
(choquet-expected) utility of the quality which is o
ered on the market, i.e.
10
he chooses his strategies according to the decision rule given by
accept (yes) () p a CE t]
C
p
(3)
reject (no) () p > a CE t]
C
p
with
CE t] = 1 (H jp) H + 1 (t 2 fH M gjp) ; 1 (H jp)] M
p
(4)
+ 1 ; 1 (t 2 fH M gjp)] L)
2.2.1 Pooling equilibrium
By decision rule (3) the consumer accepts a pooling price o
er p if2
p a CE t]
C
(5)
p
For the seller a price o
er is only optimal if the price leads to a higher utility
for all quality grades than withdrawing from the market, i.e. if
p
a H
(6)
S
With updating rule for capacities (Eichberger and Kelsey (1999)) and an offered price p satisfying (5) and (6) the beliefs of the consumer are given by
1
1
1 (H jp) = ((p H1 );:1 (p:) p;) (:p)
= 1; (p(H:)p)
1
H M gg :p) ; 1 (:p)
1 (t 2 fH M gjp) = (f(p t) : t 2 1f;
1 (:p)
= ((p H ) + (p M ))
1 ; (:p)
11
(7)
(8)
In equilibrium the additive probability distribution equals the distributional
strategy played in equilibrium of the game with additive distributional strategies. With behavioral strategies b (p) = 1 and b (p) = 0 for p 2 S1 and p 6= p
(t 2 fL M H g) according to equilibrium conditions (A.8) (cf. appendix A) in
t
t
equilibrium updated beliefs (7) and (8) are given by
1 (H jp) = q
1 (t 2 fH M gjp) = (q + q )
(9)
(10)
H
H
M
and the choquet-expected-utility is
CE t] = (q H + q M + q L) + (1 ; ) L
p
H
M
L
(11)
Thus, with an o
ered price p following beliefs constitute a pooling equilibrium:
8
>>
>>
1
S = S1 T = T1
>>
<
1 (S T ) = >
if
>>
>> P P >: b (s1) q S S1 T T1
s1
2S t2T
t
(12)
t
with b (p) = 1 and b (p) = 0 (p 6= p) 8t 2 T1
t
t
8
>>
>> 1
a H p a CE t]
><
2
(yes) = > if
>>
>>
: 0 a CE t] < p a H
(13)
2 (no) = 1 ; 2 (yes)
(14)
S
C
p
p
C
p
p
C
p
12
In equilibrium expected quality for a credence good is not given by average
quality t = q H + q M + q L as with a experience good. Rather, expected
H
M
L
quality always lies between minimum quality L and actual average quality t.
Only for full trust in information ( = 1) the consumer's quality expectation
equals average quality.
Out o
equilibrium, i.e for an o
ered price p a H with p 6= p, updated
beliefs are 1 (H jp) = 0 since (p H ) = b (p) q = 0 q .3 Such an o
er is
C
H
H
H
only accepted if p a L by condition (5). In this case, only the low seller
type wants to sell and this price o
er is not played in a pooling equilibrium.
C
With equilibrium conditions (12), (13) and (14), a price o
er leads only to a
successful transaction if the combination
t := CE t] = (q L + q M + q H ) + (1 ; ) L
p
L
M
(15)
H
of average quality and minimum quality is valued high enough by the consumer. The less the consumer trusts in information about quality, i.e. the
probability distribution over types, the more pessimistic is the consumer and
the decision will be based only on the minimum quality L.
For a successful transaction the price o
er must be adequately adapted. With
2 0 1) one yields CE t] < E t] and the equilibrium price for a credence
good is always lower than the equilibrium price for an experience good of
equivalent quality. Full condence in information ( = 1) yields CE t] = E t]
and the price o
er can be maximal, i.e. p = p := a E t], with p the
price o
er for an experience good (cf. appendix A).
p
p
p
EG
13
C
p
p
EG
p
aC
p
6
H
aC
aS
t
EG
p
aS
1
H
p
2
t
L
M
t2
tp
t 1
H
t
t
Fig. 1. Pooling equilibrium with credence goods
Figure 1 illustrates the equilibrium conditions. A transaction is only possible
if the price p, which is o
ered for a credence good, is not higher than the
consumer's value for actual average quality E t], i.e. if p 2 a H p ]. For
trust in information large enough, i.e. = 1, according to condition (13) there
p
S
EG
exists an intervall a H p1 ] in which a price p can lie to enable a transaction.
To yield maximal possible utility the seller demands a price p1 > a H . If
S
S
trust in information is too low, i.e. = 2, one yields p2 < a H . Hence,
there is no intervall of possible prices, which leads to a transaction since in
equilibrium according to (13) an accepted price satises p a H .
S
S
14
2.2.2 Semi-pooling equilibrium
If the seller's types do not choose same decisions two equilibrium situations
arise:
(1) Low and medium seller type pooling: The low and medium seller type
are pooling with a price p, and the high seller type is choosing n , i.e. he
withdraws from the market.
(2) Medium and high seller type pooling: The high and medium seller types
are pooling with n , i.e. they do not o
er their good, and the low seller
type plays a price o
er p.
p
p
Low and medium seller type pooling. A price for which high quality is
not o
ered must lead to zero utility for the high seller type, i.e. the price must
satisfy
p<a H
(16)
S
Since only low and medium quality is o
ered such a price is accepted if
p a M and p a CE t]
C
C
p
(17)
A price o
er is optimal for the seller if it is optimal for both types L and M ,
i.e. if p a L and p a M and therefore
S
S
p
a M
(18)
S
As before, in equilibrium updated beliefs are based on the equilibrium strategies of the game with additive probabilities. Since only sellers of low and
15
medium quality want to sell this equilibrium strategies are given by b (p ) = 0
and b (n ) = 1 and b (p ) = b (p) = 1 for p 2 a M a M ] (condiH
H
p
L
S
M
C
tion A.13, appendix A). Updated beliefs and choquet-expected-utility then
are given by
1 (H jp) = 0
1 (t 2 fH M gjp) = 1 ; q q
8>
>> E t] = 1
>>
<
CE t] = >
if
>>
>>
: L =0
(19)
(20)
M
H
p
(21)
p
Thus, following beliefs constitute an equilibrium in which sellers of low and
medium quality are o
ering their good for a price p :
8
>>
>>
1
S = S1 T = T1
>>
<
1 (S T ) = >
if
>>
>> P P b (s1) q S S1 T T1
: s1
2S t2T
t
(22)
t
with b (p) = 1 if t 2 fL M g and b (n ) = 1 if t = H
8>
>> 1
a M p a CE t]
>>
<
2 (yes) = > if
>>
>>
: 0 a CE t] < p a M
t
t
S
C
p
p
C
p
(23)
C
2 (no) = 1 ; 2 (ja)
p
p
(24)
p
16
p
aC
aS
aC
6
H
H
aC
aS
t
t
M
p
EG
p
aS
1
M
p
2
L t2 tsp
t1
tp
M
t
t
H
Fig. 2. Semi-pooling equilibrium with two seller types
A price p 6= p out o
equilibrium (p < a H not satisfying equilibrium
S
conditions (22), (23), and (24)) leads to 1(t 2 fH M gjp) = 0. This price
only is accepted if by (17) p a L. However, this price is not o
ered by
C
the medium seller type and therefore is not played. For p a H the price
S
can be accepted if conditions (12), (13) and (14) for a pooling equilibrium are
satised.
Figure 2 illustrates the equilibrium conditions. A price p < a H is part of
S
an equilibrium only if p is less or equal than the consumer's value of o
ered
average quality t = L+1 M (q L + q M ), i.e. if p satises p 2 a M p ]
with p the equilibrium price for an experience good.
q
q
L
M
EG
17
S
EG
If trust in information is suciently large ( = 1, cf. gure 2) with condition
(23) there is an interval a M p1 ] of price o
ers leading to a transaction.
S
To enforce the maximum in possible prot the seller plays p = p1 > a M .
However, if trust in information is too low ( = 2, cf. gure 2), p2 < a M .
S
S
Since an equilibrium must satisfy p a M according to (23) there is no
S
equilibrium with such an price o
er.
Medium and high seller type pooling. Low quality is exclusively o
ered
if withdrawing is optimal for the medium and high seller type, i.e. if a price
p satises p < a M . The consumer rejects this price o
er, if p > a L.
He accepts if p a L and p CE t]. The price o
er is optimal for the
remaining seller type if p a L.
S
C
C
p
C
For an equilibrium price o
er p beliefs in the game with additive beliefs satisfy
b (p) = 1 and b (p ) = b (p) = 0 and b (n ) = b (n ) = 1 (cf. condition
A.18, appendix A). Thus, consumer's beliefs are given by
M
L
M
H
p
p
H
(:p ) = b (n ) q + b (n ) q
H
p
H
M
p
(25)
M
As a consequence, updated beliefs are given by (p 2 a L a L])
S
1 (H jp) = 0
C
(26)
1 (q 2 fH M gjp ) = 0
The (choquet-)expected-utility then is given by
CE t] = 1 ; 1 (t 2 fH M gjp)] L = L
p
(27)
Thus, following beliefs and price o
er form an equilibrium, in which only low
18
quality is o
ered:
8
>>
>>
1
S = S1 T = T1
>>
<
1 (S T ) = >
if
>>
>> P P b (s1) q S S1 T T1
: 2S t2T
b (p) = 1
t
s1
(28)
t
with
if t = L and b (n ) = 1 if t 2 fH M g
2 (yes) = 1 if a L p a L
2 (no) = 1 ; 2 (ja)
t
S
p
p
t
p
(29)
(30)
C
p
Independently from trust a price o
er p 2 a L a L] is always accepted (cf.
gure 3 on page 20). To enforce maximum prot the seller plays p = a L.
S
C
C
An o
er p 6= p with p < a M not satisfying equilibrium conditions (28),
(29) and (30), is not accepted. However, an o
er p a M is accepted if
S
S
conditions (12), (13), and (14) for a pooling equilibrium or conditions (22),
(23), and (24) for a semi-pooling equilibrium are satised.
2.3 Discussion of the equilibrium conditions
In the conditions for pooling and semi-pooling equilibria deduced so far the
parameter represents the inuence of consumer's trust in given quality information about credence goods. Thus, by varying the parameter it can be
taken advantage of comparing the well known situation for experience goods
with the situation for credence goods reaching from full trust in information
with experience goods ( = 1) to the situation of complete mistrust only
possible for credence goods ( = 0).
19
p
aC
aC
aS
aS
aC
aS
6
H
aC
H
aS
t
t
M
M
L
-
L
L
tsp
M
tp
H
t
Fig. 3. Semi-pooling equilibrium with one seller type
Complete trust in information ( = 1). If the consumer trusts in the given
quality information the beliefs in our model for credence goods amount just
to the additive beliefs of the model for experience goods. Expected quality
then is given by the actual average quality o
ered on the market and the
equilibrium conditions of both models are identical. In this case, on the market
for credence goods the usual problem of adverse selection without any problem
of trust occurs: If the actually o
ered average quality t for a given price o
er
is too low in equilibrium no transaction takes place.
Market for one quality (q = 1 for exact one t 2 fL M H g and 2 (0 1)).
t
If there is only one quality o
ered in the market (q = 1 for exact one t 2
fL M H g) with full trust in given information ( = 1) the consumer accepts
t
20
p
aC
=
p
6
aC
aS
H
t
EG
p >
aS
1
H
p <
1
M t<1 t1
L
t>1
H
=
t
t
t
Fig. 4. Adverse selection with a credence good of only high quality
a price p = a t, which is equal to the maximum price o
er for a experience
good. A transaction always takes place since neither there is an information
problem nor a problem of trust (cf. gure 4).
EG
C
However, for < 1 a new source of market failure arises from the problem
of trust.4 In equilibrium a transaction takes place if there is a price p with
2 0 1) satisfying (t 2 fM H g)
a t p t = a ( t + (1 ; ) L)
S
C
(31)
With 1 as the minimum level of trust enabling such a price o
er, one yields
a L
1 = aa tt ;
;a L
S
C
C
C
(32)
21
For 2 0 1) there is no price p for which a transaction takes place (cf. gure 4 on page 21), i.e. the consumer only accepts a price p, if5 2 1 1].
Conversely, this means if trust in given information is too low no transaction
takes place and a kind of market failure arises relevant only for credence goods
(market failure by trust induced adverse selection).
To maximize prot the seller asks for a price p = a t , i.e. prot increases
with increasing trust in information.6 Conversely, for a transaction to be taken
C
place trust in information must be the much higher, the smaller is the di
erence between the consumers' value for a given quality and the seller's value
for this quality.7
The connection between trust in information and consumer's value of quality
is most clearly shown for a = const. In this case increasing consumer's value
leads to an increase of the interval a t a t + (1 ; ) a L], in which
an accepted price o
er can lie. Thus, the minimal trust 1 for a successful
S
S
C
C
transaction can be smaller:8 the higher value of quality leads even for low
trust to positive consumer's utility, i.e. the higher value compensates a loss of
trust in the information.
Market for all qualities (0 < q < 1 for t 2 fL M H g and 2 (0 1)). If
t
all qualities are o
ered with probability q 6= 0 (t 2 fL M H g) with full trust
( = 1) the usual problem of adverse selection for experience qualities occurs.
However, for 2 (0 1) transaction only takes place under two conditions.9 On
the one hand, there is a pooling equilibrium if all qualities are o
ered and the
t
price o
er p satises
a H p a (q H + q M + q L) + (1 ; ) L]
S
C
H
M
22
L
(33)
On the other hand, there is a semi-pooling equilibrium if high quality is not
o
ered and the price o
er p satises
i
h a M p a L + q 1; ; H + (1 ; ) L
M
S
C
M
(34)
L
q
Dening 2 as the minimum level of trust, leading to a transaction with q 6= 0
t
(t 2 fL M H g) for a given quality distribution, in a pooling equilbrium 2
satises
a L
2 = 2 := a (q H +a q H ;
M + q L) ; a L
S
p
C
H
(35)
C
M
L
C
and in a semi-pooling equilibrium 2 satises
2 = 2 := (a M ; a La) qM ;+ a(a LH ; a L) q
S
sp
C
C
C
M
S
S
H
(36)
As shown in gure 5 on page 24, a pooling price o
er for all seller types only
exists if 10
2 2 1]
(37)
p
Compared to a market with only high quality o
ered (cf. gure 4 on page 21)
condition (32) with t = H and (35) leads to
2 > 1
(38)
p
Thus, in the situation with all quality levels o
ered on the market trust in
information must be higher for a successful transaction than in the situations
with only high quality o
ered. Conversely, in the situation with all quality
levels o
ered and the level of trust not high enough to enable a transaction
a low level of trust can be compensated and a transaction can take place if
23
p
aC
p
6
H
aC
aS
t
EG
p
p
>
2
aS
p
H
<
p
t
2
L
p p
M t < t
2
2
t >
p
2
t
H
t
Fig. 5. Adverse selection with a credence good of dierent qualities
an adequate high quality is guaranteed, i.e. guaranteeing only quality t with
t = H . This means, actions of guaranteeing a certain quality can enforce or
even substitute actions of gaining or increasing trust.
The seller yields maximum prot by demanding a price p = a t with
p < p . The higher is consumer's trust in the given probabilities of quality
distribution, the higher this price will be, i.e. a price o
er and the resulting
possible prots are lower than with full trust in given information ( = 1).
C
EG
Conversely, as with the situation of only one quality level, for a relative increase of a the consumer's trust in the distribution of quality must increase
if a transaction should take place. Additionally, the trust in the quality distriS
24
bution must be the higher, the lower is the probability of only high quality on
the market.11 If average quality on the market is decreasing already a small
deviation from full trust makes transaction impossible.
A semi-pooling price o
er with which only sellers of low and medium quality
o
er only exists if12 2 2 1]. For only one quality condition (32) with
t = M and (36) yields
sp
2 > 1
(39)
sp
Thus, for a transaction to take place a higher level of trust in information is
needed. Conversely, as in the situation of a pooling price o
er, this leads to a
possible compensation of actions of producing trust by actions of guaranteeing
higher quality. For the given situation this actions are actions of guaranteeing
only quality t = M .
Complete mistrust (0 < q < 1 ^ = 0). If the consumer does not trust
in the seller at all ( = 0), a transaction with o
ered quality other than L
will never take place (cf. gure 3 one page 20): The consumer would accept
a price o
er p only, if the seller demands a price p =0 a L. But with
this price for sellers of medium and high quality, respectively, withdrawing
from the market is optimal. Thus, only an equilibrium exists with the seller
C
only o
ering low quality. As a consequence, there is a complete failure of the
market with o
ering medium and high quality caused solely by the problem
of trust given with credence goods.
25
3 Conclusions
Previous research on credence goods has not yet given a theoretical basis
for analyzing asymmetric information given with credence goods. In contrast,
our paper has presented a framework which integrates quality ambiguity with
credence goods and the given problem of trust into economics of information
in an adequate way.
Our model shows clearly the consequences of quality uncertainty with credence
goods for market behavior. On a market for credence goods a transaction does
not solely depend on the quality o
ered by a seller, but trust in the given information about the quality distribution plays the crucial role. With experience
goods only average quality o
ered on the market determines whether a transaction takes place or not. In contrast, for credence goods consumers' quality
expectation which consumers are using for the decision, always is lower than
the actual average quality because of the specic problem of trust. As a consequence, a new source of market failure only given with credence goods arises:
If trust in quality information is too low only seller types of the lower qualities
have got an incentive to o
er their good and higher quality is driven out o
the the market (market failure by trust induced adverse selection). Even if
transaction takes place in equilibrium possible prices for a credence good are
always lower than prices for an equivalent experience good.
Generally, the framework suggests a di
erence in the specic causes for market
failure with credence goods and experience goods. With credence goods it is
not only the lack of information which leads to ineciency or even market
failure. As a entirely new factor, it is the degree of trust in given information,
26
represented by the ambiguity of own beliefs (parameter in our model) about
the existence of the relevant quality, which emerges for credence goods. Even
if quality of a credence good and an experience good is in fact the same
quality expectation for a credence good is lower than for an experience good.
This lack of trust can lead to market failure with credence goods even if with
experience goods there would be a transaction. Only if consumers have full
trust in information quality expectations are identical for credence goods and
experience goods, and causes for market failure are identical.
With the inuence of trust becoming obvious, the model also gives hints to
overcome the problem of trust. If high quality is driven out o
the market
because of lack of trust trust building actions can be replaced by actions of
guaranteeing quality: As well on markets, on which higher quality is guaranteed,13 as on markets on which consumers value quality higher a lower trust
in information about quality is needed for a transaction to take place.
27
Notes
For a rst attempt to exploid the decision theoretic conditions of search,
experience and credence goods cf. Becker (1997).
1
An o
er with p < a L is always accepted and an o
er with p > a H
is never accepted.
2
C
C
With updating rule for capacities, beliefs can be determined out o
the
equilibrium path, too (Eichberger and Kelsey (1999)).
3
Since with t = L the equilibrium conditions are independent of quality
information this is only valid for t 2 fM H g.
4
With a t ; a L > 0 for t 2 fM H g and
S ; C 1.
C ; C
5
C
a
t
a
L
a
t
a
L
6
7
C
C
S
a
a
H
L
it follows 0 With a t a t for 2 0 1] and t =1 = t prot is maximal for = 1.
C
C
For a = a one yields 1 = 1.
8
@
C
@a
C
S
S t;aC L
aC t;aC L
a
< 0.
Since with t = L the equilibrium conditions are independent of trust in
information only qualities t 2 fM H g are relevant.
10
2 1 for CS .
p
11 ( 2 )
< 0.
9
p
@
a
t
a
H
H
@q
12 aS
C
a
L
+qM (M ;L)
;qH (H ;L)
M
=) 2 1.
sp
In fact, a private guarantee of the seller would su
er from the same problem of trust and would therefore not be sucient. Only a guarantee given by
an independent third party would solve this problem.
13
28
Appendix
A Adverse selection with experience goods
Consider a market with a consumer and a seller for goods of three di
erent
qualities:14 With probabilities q (t 2 fL M H g) a good is of quality t with
L M H 2 IR+ L < M < H . Since the good is an experience good only the
seller knows the quality before purchase. The consumer has to use the price
as the only signal for quality.
t
For the consumer valuation of quality t is given by a t (a 2 IR+) and
a t (a 2 IR+, a < a ) for the seller. It is assumed that the consumer does
not value a specic quality level higher than the seller values the next higher
quality level, i.e. CS < and CS < . Additionally, the consumer values
a given quality always more than the seller, i.e. a < a . Thus, a purchase
would be desirable if the consumer was knowing the true quality.
C
S
S
S
C
C
a
M
a
H
a
L
a
M
S
C
Each seller type either can o
er his good on the market and ask for a price
p 2 IR+, or can withdraw from market (n ), i.e. the strategy set S1 of the
seller is given by S1 = IR+ fn g. The consumer observes the prices and can
p
p
reject or accept the o
er, i.e. the strategy set S2 of the consumer is given by
S2 = fyes nog.
If the consumer rejects an o
ered price p he yields zero utility and the seller
yields a utility of a t (t 2 T1). Given a quality t, accepting an o
er the
S
consumer yields an utility of a t ; p and the seller receives the price p. By
withdrawing from the market at a quality t, the consumer always gets zero
utility and the seller yields a utility of a t.
C
S
29
aS
0
H
np
yes
p
no
;
M
;
H
p
Hp
H
p aC
p aC
aS
0
H
qH
p
yes
p
qM
M
Mp
aS
0
no
H
np
qL
aS
M
yes
0
p aC
;
L
p
Lp
L
no
np
aS
aS
0
L
0
L
Fig. 6. Adverse selection as extensive form game
In the extensive form of the game (cf. gure 6) for each player i (i = 1 2)
J is the set of information sets with J1 = fJ1 J2 J3 g and information sets
J1 = fLg, J2 = fM g and J3 = fH g and J2 = fJ : p 2 IR+g J p with
i
p
n
J = fH M L g. b are the behavioral strategies for each player i, i.e. b1 :
J1 ! B with b1 (J1 ) = (b (p) b (n )), b1 (J2 ) = (b (p) b (n )) and b1 (J3 ) =
(b (p) b (n )), and b2 : J2 ! B with b2 (J ) = (b (yes) b (no)) and b2 (J p ) =
(b p (yes) b p (no)).
p
p
p
p
i
L
H
n
H
L
p
M
p
p
p
M
p
p
n
n
The consumer's decision depends on the conditional beliefs for receiving a good
of a quality t given a price p. With (L) = P (t = Ljp), (M ) = P (t = M jp)
and (H ) = P (t = H jp), respectively, the consumer yields a expected utility of
(L) 0 + (M ) 0 + (H ) 0 = 0 if he rejects the o
er. The consumer accepts
a price if the price is greater than his valuation of expected quality, i.e. with
30
p
the conditional expectation
E t] := (L) L + (M ) M + (H ) H
(A.1)
p
his decision rule is given by
accept (yes) () p a E t]
C
p
(A.2)
reject (no) () p > a E t]
C
p
Equilibrium strategies can be distinguished according to the seller's types
playing same prices (pooling or semi-pooling equilibrium) or playing di
erent
prices (separating equilibrium).
A.1 Separating equilibrium
If each seller type asks for a di
erent price p = a t (t 2 fL M H g) the
behavioral strategies for which pay-o
s are maximized are given by b (p ) = 1,
t
C
L
L
b (p ) = 1 and b (p ) = 1. For a price p the consumer's beliefs are updated
to (t 2 fL M H g)
M
M
H
H
8
>>
>> 1
p=p
><
(t) = > when
>>
>>
:0
otherwise
t
(A.3)
Because the consumer can identify the seller's types due to prices he would
always accept a price p = p . However, this would be a incentive for both the
low and medium seller type not to play their price and to ask for the high price
H
31
p . As a consequence, a separating equilibrium with the consumer accepting
H
the price o
er does not exist.
A.2 Pooling equilibrium
With all seller's types playing the same price p behavioral strategies are given
by b (p) = 1, b (p) = 1 and b (p) = 1. Such a price is only accepted if the
price satises (A.1) and (A.2), i.e.15
L
M
H
p a ( (L) L + (M ) M + (H ) H )
(A.4)
C
For the seller, playing price p is only optimal if all seller's types yield a higher
utility than by withdrawing from market, i.e.
p
a H
(A.5)
S
An equilibrium price must satisfy (A.4) and (A.5) and for the quality in equilibrium t0 2 fL M H g beliefs are given by (p 2 a H a H ])
S
C
0
0
(t0) = b (p) q + bb ((pp)) qq + b (p) q
=q 0
t
L
L
t
M
M
H
H
t
(A.6)
With (A.4) a pooling price p 2 a H a H ] is only accepted if
S
C
p a E t] = a (q L + q M + q H )
C
p
C
L
M
H
(A.7)
For a price p a (perfect Bayes-Nash) equilibrium then is given by the following
32
beliefs and behavioral strategies:
b (p) = 1 t 2 fL M H g
t
b (n ) = 0 t 2 fL M H g
t
(t)
p
= q t 2 fL M H g
t
8
>>
(A.8)
>> 1 a H p a (q L + q M + q H )
><
b (yes) = > for
>>
>>
: 0 a (q L + q M + q H ) < p a H
S
C
L
M
H
p
C
L
M
H
C
b (no) = 1 ; b (yes)
p
p
If the seller is indi
erent between playing a price and withdrawing from market
the equilibrium conditions assume that he prefers playing the price. Out o
equilibrium, for prices p 2 a L a H ) beliefs must be (L) = 1 to support
equilibrium.
S
S
A.3 Semi-Pooling equilibriums
Because of the possibility to withdraw from market there are semi-pooling
equilibria, in which the seller only separates for types in subsets of the entire
set of types, i.e. neither all types demand the same price nor each single type
demands a di
erent price.
In the given game the structure of semi-pooling equilibria is determined by the
willingness of the seller's types only to sell for prices equal to their valuation
of the good. Additionally, it is assumed that each type of seller only prefers
33
withdrawing from market if a price demand is lower than its valuation of the
good playing a price demand greater then its valuation is preferred if this price
is not accepted. For a price p to be accepted only the types t 2 fL M H g
remain on market for which a t < p. This price is played by all types and
S
constitutes a pooling price strategy. A type t with a t p withdraws from
S
market.
Possible equilibria are determined by the following combinations
(1) Low and medium seller type pooling: The L-type and M-type are pooling
with a price p and the H -type plays n , i.e. withdraws from market.
An equillibrium with the H-type and M-type pooling can be disregarde,
because in this case the L-type would play this price, too.
(2) Medium and high seller type pooling: The H-type and the M-type are
pooling with n and the L-type plays p.
p
p
Low and medium seller type pooling. The H-type does not o
er on the
market if the price satises p < a H . Because of no H-quality on the market
a price p is accepted if
S
(A.9)
p a M and p E t]
C
p
For the remaining types price is optimal if16
p
a M
(A.10)
S
With a price p satisfying (A.9) and (A.10) and strategies b (p) = b (p) = 1
and b (p) = 0 updated beliefs amount to
L
M
H
q
(L) = q +
q
(A.11)
L
L
M
34
and (M ) = L+M M and (H ) = 0 (p 2 a M a H )), respectively. Expected
utility then is given by
q
q
E t] =
p
S
q
S
(A.12)
(q L + q M ) < a H
1
L +qM
L
q
M
S
Together with a price p the following behavioral strategies and beliefs determine a (perfect Bayes-Nash) equilibrium
8
>>
>> 1 t 2 fL M g
><
b (p) = > if
>>
>>
:0 t = H
8
>>
>> 0 t 2 fL M g
><
b (n ) = > if
>>
>>
:1 t = H
8
>>
>> L+t M t 2 fL M g
><
(t) =
if
>>
>>
>: 0
t=H
8
>>
>> 1 a M p a ( L+L M L + L+M M M )
><
b (yes) = > if
>>
>>
: 0 a ( L+L M L + L+M M M ) < p a M
t
t
p
q
q
q
q
S
C
q
q
q
q
q
p
q
C
q
q
q
q
b (no) = 1 ; b (yes)
p
p
35
q
C
(A.13)
To maximize prot the seller plays p = a ( L+L M L + L+M M M ). Out o
the equilibrium path equilibrium is supported by beliefs (L) = 1.
q
C
q
q
q
q
q
Medium and high seller type pooling. Only L-quality is o
ered on the
market, if p < a M . The consumer accepts a price p if
S
(A.14)
p a L and p E t]
C
p
If p satises
p
a L
(A.15)
S
the price is optimal for the only remaining type of seller. Because only the Ltype o
ers on the market strategies are given by b (p) = 1 and b (p) = b (p) = 0.
With a price satisfying (A.14) and (A.15) the consumer's beliefs are given by
L
L
(A.16)
(L) = 1 if p 2 a L a L]
S
M
C
and (H ) = (M ) = 0 (p 2 a L a M )). Expected utility is then given by
S
S
E t] = a L:
p
(A.17)
C
36
An equilibrium is given by a price p 2 a L a L] and behavioral strategies
with beliefs satisfying
S
C
8
>>
>> 1
t=L
><
b (p) = > if
>>
>>
: 0 t 2 fM H g
8>
>> 0
t=L
>>
<
b (n ) = > if
>>
>>
: 1 t 2 fM H g
8
>>
>> 1
t=L
><
(t) = > if
>>
>>
: 0 t 2 fM H g
t
t
p
(A.18)
b (no) = 1 ; b (yes)
p
p
To maximize prot the seller plays a price p = a L. Out o
the equilibrium
path beliefs (L) = 1 support the equilibrium.
C
37
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41
Bisher in der Reihe Hohenheimer Agrarökonomische Arbeitsberichte erschienen:
Becker, T.; Benner, E (2000): Zur Problematik der Herkunftsangabe im regionalen Marketing
Arbeitsbericht Nr. 1
Chaipan, C. (2000): The Euro and its Impact on ASEAN Economies
Arbeitsbericht Nr. 2
Henze, A. (2000): Marktwirtschaft - Wirtschaftliche Freiheit, motiviertes Handeln und
Wettbewerb: Quellen des Wohlstands
Arbeitsbericht Nr. 3
Benner, E. (2000): Zur effizienten Herkunftsangabe im europäischen Binnenmarkt
Arbeitsbericht Nr. 4
Vorgrimler, D. (2000): Wettbewerbstheorie und stagnierende Märkte
Arbeitsbericht Nr. 5
Beerbaum, S. (2001): Grundzüge einer internationalen Zusammenarbeit im Klimaschutz aus
ökonomischer Sicht
Arbeitsbericht Nr. 6
Vorgrimler, D.; Wübben, D. (2001): Prognose der Entwicklung des Agrartechnikmarktes Eine Expertenbefragung nach der Delphi-Methode
Arbeitsbericht Nr. 7
Tesch, I. (2003): Informationsbedarf und Informationsbeschaffung von Konsumenten bei
Lebensmitteln pflanzlicher Herkunft - Eine empirische Untersuchung anhand von FokusGruppen Arbeitsbericht Nr. 8
jeweils als pdf-file unter: http://www.uni-hohenheim.de/marktlehre/berichte/wpaper.html